Progressive network recovery is the problem arising when a network is subject to massive failures and the network operator has to identify the optimal sequence of repair actions to maximize carried traffic. As initial deployments of quantum-key-distribution (QKD) over optical networks start appearing in several locations worldwide, in this paper, for the first time, we model and solve the Progressive QKD Network recovery (PQNR) problem in QKD networks to accelerate the QKD network recovery after massive failures. Specifically, we formulate an Integer Linear Programming (ILP) model to model the achievable key rate for different QKD network architectures (w/o trusted relay and optical bypass). Due to the scalability issue of ILP, we also propose a scalable heuristic to solve the PQNR problem for large topologies. Our numerical results show that joint utilization of optical bypass and trusted node technologies leads to significant improvement in performance and that our heuristic solution has an acceptable optimality gap compared with ILP while reducing time.
Progressive network recovery is the problem arising when a network is subject to massive failures and the network operator has to identify the optimal sequence of repair actions to maximize carried traffic. As initial deployments of quantum-key-distribution (QKD) over optical networks start appearing in several locations worldwide, in this paper, for the first time, we model and solve the Progressive QKD Network recovery (PQNR) problem in QKD networks to accelerate the QKD network recovery after massive failures. Specifically, we formulate an Integer Linear Programming (ILP) model to model the achievable key rate for different QKD network architectures (w/o trusted relay and optical bypass). Due to the scalability issue of ILP, we also propose a scalable heuristic to solve the PQNR problem for large topologies. Our numerical results show that joint utilization of optical bypass and trusted node technologies leads to significant improvement in performance and that our heuristic solution has an acceptable optimality gap compared with ILP while reducing time.
With progressive network recovery, operators restore network connectivity after massive failures along multiple stages, by identifying the optimal sequence of repair actions to maximize carried live traffic. Motivated by the initial deployments of quantum-key-distribution (QKD) over optical networks appearing in several locations worldwide, in this work we model and solve the progressive QKD network recovery (PQNR) problem in QKD networks to accelerate the recovery after failures. We formulate an integer linear programming (ILP) model to optimize the achievable accumulative key rates during recovery for four different QKD network architectures, considering different capabilities of using trusted relay and optical bypass. Due to the computational limitations of the ILP model, we propose a deep reinforcement learning (DRL) algorithm based on a twin delayed deep deterministic policy gradients (TD3) framework to solve the PQNR problem for large-scale topologies. Simulation results show that our proposed algorithm approaches well compared to the optimal solution and outperforms several baseline algorithms. Moreover, using optical bypass jointly with trusted relay can improve the performance in terms of the key rate by 14% and 18% compared to the cases where only optical bypass and only trusted relay are applied, respectively.
By overcoming the distance limit in quantum key distribution (QKD) technology, key relaying over trusted nodes is regarded as an essential function for practical quantum-secured networking. The key relay function consumes a series of costly quantum key resources to establish an end-to-end key in QKD networks (QKDNs); thus, an efficient key relay algorithm is required. To investigate this problem, we developed an integer linear programming (ILP) formulation that maximizes a balanced summation between max-min fairness and efficiency in the key relay. Inspired by the ILP model, this study developed a key-count differential-based proactive key relay (DPKR) heuristic algorithm to provide a scalable solution for key relays in QKDNs. The proposed DPKR algorithm iteratively selects a set of nodes by considering the key-count differential between nodes and establishes an end-to-end key by relaying it over the selected nodes. Owing to the proactive key relay model, an effective key relay route in the key management layer in the QKDN can be calculated solely by the key-count status in the key management layer. The proposed DPKR algorithm reduces manifold order-of-magnitude in the algorithm computation time at the cost of an acceptable loss in the average and minimum numbers of keys from those of the ILP optimization model. The computation time evaluation clearly manifests a scalability of the DPKR algorithm in quantum-secured networking.
As the number of attacks increases in optical networks, security at the management layer (ML) of these networks is of paramount importance to ensure that critical network management information is securely transmitted between ML node(s) and the rest of the network nodes. This work considers the problem of developing a quantum key distribution (QKD) framework for the management layer of an optical network, so that a set of management nodes can securely communicate and exchange keys with the network nodes. An integer linear program (ILP) is formulated for the design of a management layer - quantum key distribution (ML-QKD) network, aiming to maximize the transmission rates provided to network and management nodes, by optimally selecting the placement of the management node(s) and QKD systems. Performance results for several scenarios with a different number of available management nodes and QKD systems, demonstrate that the proposed formulation can design an optimal ML-QKD network.
Quantum Key Distribution (QKD) is currently being explored as a solution to the threats posed to current cryptographic protocols by the evolution of quantum computers and algorithms. However, single-photon quantum signals used for QKD permit to achieve key rates strongly limited by link performance (e.g., loss and noise) and propagation distance, especially in multi-node QKD networks, making it necessary to design a scheme to efficiently and timely distribute keys to the various nodes. In this work, we introduce the new problem of joint Routing, Channel, Key-rate and Time-slot Assignment (RCKTA), which is addressed with four different network settings, i.e., allowing or not the use of optical bypass (OB) and trusted relay (TR). We first prove the NP-hardness of the RCKTA problem for all network settings and formulate it using a Mixed Integer Linear Programming (MILP) model that combines both quantum channels and quantum key pool (QKP) to provide an optimized solution in terms of number of accepted key rate requests and key storing rate. To deal with problem complexity, we also propose a heuristic algorithm based on an auxiliary graph, and show that it is able to obtain near-optimal solutions in polynomial time. Results show that allowing OB and TR achieves an acceptance ratio of 39% and 14% higher than that of OB and TR, respectively. Remarkably, these acceptance ratios are obtained with up to 46% less QKD modules (transceivers) compared to TR and only few (less than 1 per path) additional QKD modules than OB.
Quantum Key Distribution (QKD) is a recent technology for secure distribution of symmetric keys, which is currently being deployed to increase communications security against quantum attacks. However, the key rate achievable over a weak quantum signal is limited by the link performance (e.g., loss and noise) and propagation distance, especially in multi-node QKD networks, making it necessary to design a scheme to efficiently and timely distribute keys to the various nodes. In this work, we formulate, using a Mixed Integer Linear Programming (MILP) model, a novel Routing, Channel, and Key-rate Assignment (RCKA) problem for QKD with Quantum Key Pool (QKP), which exploits the opportunity of using trusted relays and optical bypass. Our formulation accounts for the possibility to build a quantum key distribution path that combines both quantum channels and trusted relays to increase the acceptance ratio of key rate requests. Leveraging different versions of the proposed MILP model, we evaluate several strategies exploiting different combinations of trusted relays and optical bypass for the RCKA problem. Results show how different trade-offs between security and resource-efficiency (expressed in terms of acceptance ratio of key rate requests vs. key storing rate in QKP) can be achieved when adopting trusted-relay and/or optical-bypass technologies. Trusted relays can provide a higher acceptance ratio when the number of QKD modules (transmitters or receivers) is sufficiently large, while optical bypass, which does not require the implementation of expensive trusted relays, is preferable when the number of QKD modules is a limiting factor.
Quantum Key Distribution (QKD) technology leverages its inherent security advantages to ensure information-theoretic security for data transmission in networks. However, existing QKD networks still face critical challenges, including network congestion that stems from limited key resources and uneven resource allocation methods. Thus, in this paper, we focus on the issue of network congestion caused by bottleneck links and aim to achieve load balancing. Considering the limited key resources, we first introduce the key resource utilization ratio as an indicator of bottleneck links and formulate the resource allocation problem as an Integer Linear Programming (ILP) problem. To deal with the complexity of the ILP problem, especially in large-scale network scenarios, we design a heuristic algorithm that can obtain near-optimal solutions within polynomial time. Finally, we implement the proposed key resource allocation scheme in various real-world network topologies using a full-stack quantum network simulator. Compared to the existing algorithms, extensive results show that our method can reduce key resource consumption by up to 50% on bottleneck links and improve the robustness of QKD networks when facing burst quantum key agreement requests.